| Meaning: |
Modeling of sources with multiple states (usually 2 - 5) in ATM networks |
| Description: |
A GMDP comprises a state machine with \(m\) states:
-
In state \(i\) arrivals occur in constant intervals \(d_i\). If \(d_i<0\) it
is a silence state without arrivals. In that case \(-d_i\) describes the
virtual slot duration in this state.
-
\(X_i\) representing the number of arrivals in state \(i\) is arbitrarily
(discretely) distributed (often shifted geometrically -> MMDP); in the
silence state \(X_i\) means the number of time slots of the silence phase.
-
After \(X_i\) arrivals incl. an additional interval of the length \(d_i\) (or
after \(X_i\) slots of the length \(-d_i\) in the silence state), a
transition occurs to the state \(j\) with the probability \(p_{ij}\).
-
According to definition: \(p_{ii} = 0\) and \(\sum\limits_{i=1}^m p_{ij} =1\)
|
| Parameters: |
-
number of states \(m\)
-
transition probabilities \(p_{ij}\)
-
distribution of the number of arrivals \(X_i\) in the individual states
-
arrival intervals \(d_i\) in the individual states
|
| Characteristic values: |
Moments and distribution of the arrival intervals |
| Parser example: |
[...].Dist = GMDPDistribution
[...].Dist.States = 3
[...].Dist.PMAP = [ [0 0.5 0.5] [0.5 0 0.5] [0.5 0.5 0] ]
[...].Dist.PhaselengthDistribution_0 = ShiftedGeometric
[...].Dist.PhaselengthDistribution_0.Mean = 10
[...].Dist.PhaselengthDistribution_1 = ShiftedGeometric
[...].Dist.PhaselengthDistribution_1.Mean = 10
[...].Dist.PhaselengthDistribution_2 = ShiftedGeometric
[...].Dist.PhaselengthDistribution_2.Mean = 5
# negative value denotes silence state
[...].Dist.InterCellTimes = [ -1 2 4 ]
|
| References: |
-
P. J. KÜHN: Reminder on queueing theory for ATM networks. Telecommunication
Systems, No. 5, 1996, pp. 1-24.
-
G. D. STAMOULIS, M. E. ANAGNOSTOU, A. D. GEORGANTAS: Traffic source models
for ATM networks: a survey. Computer Communications, Vol. 17, No. 6, Juni,
1994.
-
T. THEIMER: How to compute the moments of a GMDP, RACE 1022, Document
UST_123_0023_CD_CC, 1989.
|